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## Solving 1/2x^-1/2 = 1/8

Can somebody please go through the steps of solving this:

$$\frac{1}{2} x^{-1/2} = \frac{1}{8}$$

The calculator says it's 16 but I keep getting the following answer:

$$\frac{1}{16}\$$

I took the liberty of rewriting your equation using the easier to read MathJax formula. Is this what you meant?

To solve the following equation for x:

$$\frac{1}{2} x^{-1/2} = \frac{1}{8}$$

Steps:

1. Multiply both sides of the equation by 2 to remove the 1/2 in front of the x. This gives us:

$$\frac{1}{2} x^{-1/2} * 2 = \frac{1}{8} * 2$$

1. Simplify it (because 1/2 * 2 = 1 and 1/8 * 2 = 1/4):

$$x^{-1/2} = \frac{1}{4}$$

1. Now to solve x for a negative index, a negative index implies 1/x. Basically flip both sides. In general, the following equation is true for negative indicies:

So, therefore, it becomes:

$$x^{1/2} = 4$$

1. Now to solve for x where x^(1/2) = 4 - we can square both sides of the equation to remove the ^(1/2). Hence, we get:

$$x = 16$$

Hope that helps. Let me know if you require any additional clarification.

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